student powerpoint on linear functions

1. Linear Functions
By: Elizabeth A. and Valarie P.

2. Definition:
A function is a linear function if
F(X)=ax+b, for real numbers A and B.
When a linear function is written in the form
Ax+By=C, it is said to be in standard form.
The graph of a linear function is a straight
line. To graph a linear function, find at
least two of its ordered pairs, plot
them, and draw a line through them.

3. Examples:
• Graph 5x-2y=10
• Solution

4. Examples (cont.)
• Let x= 0.5(0)-2y= 10 • Let x= 0will give us
• -2y= 10 the y-intercept
• Y= -5 • Solve for y
• (0,-5)

5. Examples (cont.)
• Let y= 0.5x-2(0)= 10 • Let y= 0 will give us
• 5x= 10 the x-intercept
• X= 2
• (2,0)

6. Examples (cont.)
• Let x= 4.5(4)-2y= 10 • 3rd point is a check
• 20-2y= 10 • These points would
• -2y= -10 be plotted and a line
• Y= 5 drawn through them
to complete the
• (4,5) graph.

7. Pictures

12. This is a picture of the Chapel Bridge in
Lucern, Switzerland.
The roof of this footbridge, originally constructed in 1333, can be
modeled by a linear function. The origin is set at the base of the
stone tower. Given this somewhat arbitrary origin, the roof of the
bridge could be modeled by the function y = 0.25x + 2.

14. Review
Definition:
• A linear function is a polynomial of degree one. The
graph of a linear function is a straight line. The rate of
change of a linear function is called the slope of the
function. In a linear function, the average and
instantaneous rate of change are always the same.
Formula for a Linear Function:
• General Form:
• Slope-Intercept Form:
• Point-Slope Form:
• Two-Point Form:

15. Review (cont.)
• You need only two points to graph a linear function.
These points may be chosen as the x and y intercepts of
the graph for example.
• Determine the x intercept, set f(x) = 0 and solve for x.
• 2x + 4 = 0
• x = -2
• Determine the y intercept, set x = 0 to find f(0).
• f(0) = 4
• The graph of the above function is a line passing through
the points (-2 , 0) and (0 , 4) as shown below.

16. The end…